Methods and formulas for the effects table in Equivalence Test for a 2x2 Crossover Design

Let C_2k and C_1k be defined as follows:

The carryover effect is then given by:

SE

The standard error for the carryover effect is given by the following:

where S_p is the pooled standard deviation for the carryover effect, which is given by the following:

Notation

Term	Description
	Sample mean using the data C2k, k = 1, ..., n2
	Sample mean using the data C1k, k = 1, ..., n1
n2	Number of participants in sequence 2
n1	Number of participants in sequence 1
S2	Sample standard deviation of C2k, k = 1, ..., n2
S1	Sample standard deviation of C1k, k = 1, ..., n1

The treatment effect is given by:

SE

The standard error for each effect is given by the following:

where S_p is the pooled standard deviation which is given by the following:

Notation

Term	Description
	Sample mean for sequence i (for more information, go to Methods and formulas for common concepts used in Equivalence Test for a 2x2 Crossover Design)
ni	Number of participants in sequence i
S1	Sample standard deviation of for sequence i

The period effect is given by:

SE

The standard error for each effect is given by the following:

where S_p is the pooled standard deviation, which is given by the following:

Notation

Term	Description
	Sample mean for sequence i (for more information, go to Methods and formulas for common concepts used in Equivalence Test for a 2x2 Crossover Design)
ni	Number of participants in sequence i
S1	Sample standard deviation of for sequence i

T-value

The t-value for each effect is given by the following:

P-value

The p-value for each effect is given by the following:

Where t is the observed t-value and T follows a t-distribution with n₁ + n₂ - 2 degrees of freedom.

Confidence interval for equivalence

The confidence interval (CI) for equivalence for each effect is given by the following:

Notation

Term	Description
SE	Standard error for the effect (for more information, see the section on each effect)
tα/2	Upper α/2 critical value for a t-distribution with n1 + n2 – 2 degrees of freedom
α	Probability of rejecting the null hypothesis when the null hypothesis is true (also called the significance level)
ni	Number of participants in sequence i